The diffuse supernova neutrino flux

I review the status and perspectives of the research on the diffuse flux of (core collapse) supernova neutrinos (DF). In absence of a positive signal, several upper bounds exist in different detection channels. Of these, the strongest is the limit from SuperKamiokande (SK) of 1.2 electron antineutrinos cm^-2 s^-1 at 90% confidence level above 19.3 MeV of neutrino energy. The predictions of the DF depend on the cosmological rate of supernovae and on the neutrino emission in a individual supernova (spectrum, luminosity,..). Above the SK threshold, they range between 0.05 electron antineutrinos cm^-2 s^-1 up to touching the SK limit. The SK upper bound constrains part of the parameter space of the supernova rate - and indirectly of the star formation rate - only in models with relatively hard neutrino spectra, while predictions with softer spectra would need bounds stronger by about a factor of 4 to be tested. Experimentally, a feasible and very important goal for the future is the improvement of background discrimination and the resulting lowering of the detection threshold. Theory instead will benefit from reducing the uncertainties on the supernova neutrino emission (either with more precise numerical modeling or with data from a galactic supernova) and on the supernova rate. The latter will be provided precisely by next generation supernova surveys up to a normalization factor. Therefore, the detection of the DF is likely to be precious chiefly to constrain such normalization and to study the physics of neutrino emission in supernovae.